A Confidence Interval That Is Consistent and More Informative Than a Sequential Equivalence Test for a Normal Mean

Abstract

This note shows how to construct a 1 ? β level symmetric confidence interval for a normal mean θ that is consistent with and more informative than a size β sequential equivalence test of H ₀ :|θ| > δ against the alternative H_a :|θ | ≤ δ, where δ>0 is a prespecified limit of equivalence. If the null hypothesis H ₀ is rejected and so equivalence can be declared by the test, then the confidence interval is contained in the interval [? δ, δ]. If the null hypothesis H₀ is not rejected and so equivalence cannot be declared by the test, then the confidence interval contains the interval [? δ, δ]. Therefore the test and the confidence interval are consistent in rejection or non-rejection of H ₀. But the confidence interval provides extra information on the magnitude of θ, and is therefore more informative than the test.     

New Mechanistic Insights in the Cytochrome P-450 Model Reactions: Direct Identification of the Reactive Intermediates

In CH₃CN–H₂0 medium the porphyrin Fe(IV)=O and porphyrin-C₆F₅IO adduct, and tBu $\dot{\hbox{O}}$ /tBuO $\dot{\hbox{O}}$ radicals have been spectroscopically identified. The involvement of multiple reactive intermediates in C₆F₅IO oxidizing system has also been demonstrated.     

Enhanced Hydrogenation Activity and Recycling of Cationic Rhodium Diphosphine Complexes through the Use of Highly Fluorous and Weakly‐Coordinating Tetraphenylborate Anions

The effect of the nature of the anion on the performance of ionic rhodium catalysts has received little attention. Herein it is shown that the use of highly fluorous tetraphenylborate anions can enhance catalyst activity in both conventional and fluorous media. For hydrogenation catalysts of the type [Rh(COD)(dppb)][X] {COD=1,5‐cis,cis‐cyclooctadiene; dppb=1,4‐bis(diphenylphosphino)butane; X=BF₄⁻ ( 1a ), [BPh₄]⁻ ( 1b ), [B{C₆H₄(SiMe₃)‐4}₄]⁻ ( 1c ), [B{C₆H₃(CF₃)₂‐3,5}₄]⁻ ( 1d ), [B{C₆H₄(SiMe₂CH₂CH₂C₆F₁₃)‐4}₄]⁻ ( 1e ), [B{C₆H₄(C₆F₁₃)‐4}₄]⁻ ( 1f ) and [B{C₆H₃(C₆F₁₃)₂‐3,5}₄]⁻ ( 1 g )} the activity towards the hydrogenation of 1‐octene in acetone increased in the order 1c < 1b < 1e < 1a < 1d ~ 1f < 1g with 1g being twice as active as the commonly applied 1a . Despite the fluorophilic character introduced by the substituted tetraarylborate anions, the presence of some perfluoroalkyl‐substituents in the cation was still required for achieving high partition coefficients. Therefore, [Rh(COD)(Ar₂PCH₂CH₂PAr₂)][X] {Ar=C₆H₄(SiMe₂CH₂CH₂C₆F₁₃)‐4, X=[B{C₆H₃(C₆F₁₃)₂‐3,5}₄]⁻ ( 3f ); Ar=C₆H₄(SiMe(CH₂CH₂C₆F₁₃)₂)‐4 and X=[B{C₆H₄(C₆F₁₃)‐4}₄]⁻ ( 2g )} were prepared, which were active in the hydrogenation of 1‐octene, 2g even more so than 3f . Both these highly fluorous catalysts could be recycled with 99% efficiency through fluorous biphasic separation, whereas the corresponding BF₄⁻ complex of 2g ( 2a ) did not show any affinity for the fluorous phase.     

State of adsorption and coverage by overpotential-deposited H in the H2 evolution reaction at Au and Pt

By means of potential decay measurements using a digital data acquisition and computer processing system, accurate values of overpotential decay rates, dη/dt, may be obtained from which the pseudocapacitance and coverage behaviour of overpotential-deposited (OPD) H species in the cathodic H₂ evolution reaction (HER) at Au electrodes may be quantitatively derived as a function of η. The behaviour of the HER at Au is of interest in that an unusual Tafel slope value of 2.3RT/F is exhibited in acid solution while the value of alkaline solutions is the more familiar value of ca 2.32RT/F.Analysis of the overpotential relaxation behaviour on open-circuit, following interruption of cathodic polarization currents, gives an almost constant and small interfacial capacitance corresponding to a double-layer capacitance. Steady-state OPD H coverage (θ) is hence quite small (θ_H<0.3%). The Tafel slope value of 2.3RT/F requires, however, a potential-dependent H coverage determined by an H electrosorption step almost at equilibrium but with θ_H small. The rate-determining step is suggested to be surface diffusion to preferred desorption sites.Comparative results are presented for the HER at activated Pt where, contrary to the behaviour of Au, a large pseudocapacitance for OPD H is derived that may be associated with some surface hydride formation, the possibility of readsorption of H from a boundary layer supersaturated with H₂ having been minimized by electrode rotation at a sufficiently high rate of 3600 rpm.     

Light scattering in an electric field: variations of the HH(θ) component around θ = 90°

The studies of the changes ΔH_H of the H_H component of the light scattered by dilute suspensions of particles oriented by an electric field E₀ are shown to be convenient and reliable methods for obtaining simultaneous information on the electrical (μ), geometrical (ω) and optical (δ) anisotropies of the particles. Indeed, when E₀ is applied in three particular directions, which are related to the exterior and interior bisectrices of the observation angle θ, ΔH_H(θ = 90°) generally has the same sign as (?μω), (+μω) or (?μ), according to the direction of E₀. Moreover, under the same conditions, the slopes of ΔH_H(θ) versus θ are shown to be much more informative than those of $\text{ΔH}{}_{\mathrm{H}}\text{(θ)}\text{H}{}_{\mathrm{H}}\text{(θ)}$, having the sign of (?μδ), (+μδ) or (?μδω). Experiments on TMV particles illustrate in a very satisfactory manner these theoretical conclusions.     

Estimation of deuterium recoveries from each component of water-isotope mixture in continuous-flow thermal diffusion columns

The present study deals with the estimation of deuterium recovery from the separation of water-isotope mixture (H₂O-HDO-D₂O) by continuous-flow thermal diffusion. First, the equations for predicting the degrees of separation for each component in H₂O-HDO-D₂O system were derived. The recovery of deuterium (D) was then estimated from the degrees of separation of HDO and D₂O. The most important assumption in this work was that the concentrations of each component were at local equilibrium within the thermal diffusion column, i.e. H₂O + D₂O ? 2HDO. It was found that D₂O preferably transfers to the bottom end of the column, while HDO does the same for dilute feed concentration, but then transfers to the top of the column when the feed concentration of D₂O, C_3F, increases to 0.3. The maximum total recovery of deuterium from HDO and D₂O occurs at C_3F = 0.25.     

Water–Gas Shift Reaction Over Aluminum Promoted Cu/CeO2 Nanocatalysts Characterized by XRD, BET, TPR and Cyclic Voltammetry (CV)

A series of aluminum promoted Cu/CeO₂ nanocatalysts with aluminum content in the range of 0–5wt.% were prepared by co-precipitation method and examined with respect to their catalytic performance for the water–gas shift (WGS) reaction. The catalysts were characterized by XRD, BET, H₂-TPR and cyclic voltammetry (CV) techniques. The results indicate that catalytic activity increases with the aluminum content at first, but then decreases with the further increase of aluminum content. Hereinto, Cu/CeO₂ catalyst doped with 1 wt.% of aluminum shows the highest catalytic activity (CO conversion reaches 84.4% at 200 °C) and thermal stability for WGS reaction. Correlation to the results from above characterization, it is found that the variation of catalytic activity is in very agreement with that of the surface area, the area of peak γ (i.e., the reduction of surface copper oxide (crystalline forms) interacted with surface oxygen vacancies on ceria), and the area of peak C₂ and in cyclic voltammetry process), respectively. Enough evidence was found for the fact that the metallic copper (Cu⁰) interacted with surface oxygen vacancies on ceria is the active site for WGS reaction over Cu/CeO₂ catalysts.     

Study of stability and thermodynamic properties for polychlorinated dihydrophezines by density functional theory

The thermodynamic properties of 76 polychlorinated dihydrophezines (PCDPs) in the gaseous state at 298.15 K and 101.325 kPa, have been calculated using the density functional theory (the BHANDHLYP/6‐31G*) with Gaussian 03 program. Based on these data, the isodesmic reactions were designed to calculate the standard formation heat (Δ_fH^θ), standard Gibbs free energy of formation (Δ_fG^θ) of PCDPs in the gaseous state. The relations of these thermodynamic parameters with the number and position of chlorine substituents (N_PCS) were discussed, and it was found that there exist good correlation between thermodynamic parameters, including heat capacity at constant volume , entropy (S^θ), enthalpy (H^θ), free energy (G^θ), Δ_fH^θ, Δ_fG^θ, and N_PCS. The relative stability order of PCDP congeners was theoretically proposed based on the relative magnitude of their Δ_fG^θ. In addition, the values of molar heat capacity at constant pressure (C_p,m) for PCDP congeners have been calculated.     

Relationship between two characteristic diffractions and the status of cationic lanthanum species in zeolite LaNaY

By employing ex situ and in situ powder X-ray diffraction (XRD) studies, the evolution of two characteristic diffractions at 11.9° and 12.4° (2θ) with the real-time migration of cationic lanthanum species in hydrated, dehydrated, and rehydrated lanthanum-exchanged zeolite NaY (LaNaY) have been discussed thoroughly. We found that the [La(H₂O) _m ]³⁺ ions in the supercages can strengthen the (222) diffraction and reduce the (311) diffraction dramatically, and such effects disappear when [La(H₂O) _m ]³⁺ ions migrate into the sodalite cages and the hexagonal prisms. The relationship obtained shows the capability to monitor the content/location of lanthanum species in LaNaY sample by monitoring the diffractions between 11.6° and 12.8° (2θ) in its XRD pattern, and may be useful in the routine characterization of LaNaY samples in petrochemical industry, avoiding long time collection and the structure refinement of XRD patterns. Moreover, carefully designed in situ XRD characterization proves that H₂O molecules play an important role in the reversible migration of cationic lanthanum species in zeolite Y. ²⁷Al MAS NMR was also performed for validation.     

Hydrogen half-cells in molten salts. A potentiometric investigation of the systems (Pt or Au) H2O/H2, OH− in fused alkali nitrates

The potentiometric behaviour of the hydrogen electrodes (Pt or Au) H₂O-H₂, OH_–has been investigated in molten (Na_0·5, K_0·5)NO₃ at 503 K. In both cases the potential of the indifferent electrode could be expressed by the general equation [H₂O]/[H₂] [OH^–] which is different from the one expected on the basis of a Nernstian behaviour of the theoretical overall system 2H₂O+2e=H₂+2OH^–.The experimental findings are discussed in terms of mechanistic models involving the actual electrode surface and the standard potential for the theoretical (reversible) hydrogen electrode is calculated: =–·0V(versus Ag/Ag⁺ 0·07 M).     

Maximum likelihood estimation for nearly non‐stationary stable autoregressive processes

The maximum likelihood estimate (MLE) of the autoregressive coefficient of a near‐unit root autoregressive process Y_t = ρ_nY_t?1 + ?_t with α‐stable noise {?_t} is studied in this paper. Herein ρ_n = 1 ? γ/n, γ ≥ 0 is a constant, Y₀ is a fixed random variable and ε_t is an α‐stable random variable with characteristic function φ(t,θ) for some parameter θ. It is shown that when 0 < α < 1 or α > 1 and E?₁ = 0, the limit distribution of the MLE of ρ_n and θ are mixtures of a stable process and Gaussian processes. On the other hand, when α > 1 and E?₁ ≠ 0, the limit distribution of the MLE of ρ_n and θ are normal. A Monte Carlo simulation reveals that the MLE performs better than the usual least squares procedures, particularly for the case when the tail index α is less than 1.     

Positive polyacetylene electrodes in aqueous electrolytes

Polyacetylene films, contacted with platinum mesh, have been polarized anodically in aqueous H₂SO₄, HClO₄, HBF₄ and H₂F₂ of medium concentrations (30–70 wt%). Two oxidation peaks are observed, the equivalents of which are 1 $${\text{(1) 0}}{\text{.045 F mol}}^{ - {\text{1}}} {\text{ CH (2) 0}}{\text{.23 F mol}}^{ - {\text{1}}} {\text{ CH}}$$ The potential of the Process 1 decreases linearly with increasing acid concentration by 20–40 mV mol^?1 dm^?3, while the potential of Peak 2 exhibits normal Nernst behaviour (about + 60 mV decade^?1. Process 1 is partially reversible, while Process 2 is totally irreversible. From these findings for Process 1 we conclude the reversible insertion of anions into the polyacetylene host lattice, which is primarily oxidized to the polyradical cation, with the co-insertion of acid molecules HA to yield the insertion compound [(CH)⁺·yA^?·vyHA] _x y?4.5% andv=1.5 for H₂SO₄ and HClO₄. In the course of Process 2, the polymer is irreversibly oxidized according to $$( - ^ \cdot {\text{CH}} \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot ^ \oplus {\text{ CH}} - )_{x/2} + 2{\text{H}}_{\text{2}} {\text{O}} \to ( - \mathop {\text{C}}\limits_{\mathop \parallel \limits_{\text{O}} } \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \mathop {\text{C}}\limits_{\mathop \parallel \limits_{\text{O}} } - )_{x/2} + 6{\text{H}}^{\text{ + }} + 5e^ - $$ As this process occurs to some extent even in the potential region of Process 1, a continuous degradation of the host lattice occurs upon cycling.     

Influence of electrochemical treatment in phosphoric acid on the wettability of carbons

A technique developed by Studebaker and Snow was used to determine the contact angle of water (cosθ_H2O) on porous carbons which were electrochemically treated in phosphoric acid. Electrochemical oxidation resulted in a decrease in cosθ_H2O whereas, electrochemical reduction resulted in an increase in cosθ_H2O. These observations were correlated to the oxygen content of the porous carbon samples.     

Huggins' constant and unperturbed parameter of dilute polymer solutions

A novel method developed to evaluate the unperturbed parameter K_θ from the viscometric data of dilute polymer solutions can be considerably simplified by making the reasonable assumption that the Huggins' constant under theta conditions, k_Hθ, is equal to ½ for a number-average degree of polymerization of over about 2000. Two linear equations are derived pertaining to the present analysis, one to deal with the experimental data, and the other specially to estimate the intrinsic viscosity [η]θ which corresponds to κ_Hθ. All calculations were done by the linear least-squares method. The K_θ was computed by the Mark–Houwink–Sakurada equation. It is shown that reliable results on K_θ can be obtained for polystyrene and poly(vinyl acetate).     

Estimation of the Surface Energy of Polymer Solids

The methods to estimate the surface tension of polymer solids using contact angles have been reviewed in the first part. They are classified into the following three groups depending on the theories or the equations applied: (1) the methods using the Young's equation alone, (2) the methods using the combined equation of Young and Good-Girifalco, and (3) the methods using the equations of work of adhesion. Some notes and comments are given for each method and results are compared with each other. The two-liquids method for rather high energy surface is also introduced.

Next, some new possibilities to evaluate the surface tension of polymer solids are presented by our new contact angle theory in consideration of the friction between a liquid drop and a solid surface. The advancing and receding angles of contact (θ _a and θ _r ) are explained by the frictional tension γ_F and accordingly two kinds of the critical surface tension γ_C (γ_Ca and γ_Cr ) are given.

This work has shown that one of the recommendable ways to evaluate γ_S is either the maximum γ_LV cos θ_a or the maximum γ_C using the advancing contact angle θ_a alone, and another way is the arithmetic or the harmonic mean of the γ_Ca and γ_Cr . A depiction to determine the γ_C such as ln(1 + cos θ₀ ) vs. γ_LV with cos θ₀ = (cos θ₀ + cos θ_r )/2 has also been proposed.     

A tetranuclear oxofluorovanadium(IV) cluster encapsulating a Na(H2O)n+ subunit

Hydrothermal reactions of sodium vanadate, methylenediphosphonic acid, hydrogen fluoride and the appropriate organoamine yielded the vanadium(IV)-oxyfluoride compounds [NH₃(CH₂)₂(NH₂)(CH₂)₂NH₃]₃[{Na(H₂O)} ⊂ {V₄O₄F₂(O₃PCH₂PO₃)₄}]·8H₂O (1·8H₂O) and [NH₃(CH₂)₂(NH₂)(CH₂)₂(NH₂)(CH₂)NH₃]₂[{Na(H₂O)} ⊂ {V₄HO₄F₂(O₃PCH₂PO₃)₄}]·7H₂O (2·7H₂O). The vanadium-oxyfluoride cationic unit {V₄O₄F₂(O₃PCH₂PO₃)₄}^10 − of the compounds consists of pairs of fluoride bridged {VFO₅} octahedra linked through η⁴-diphosphonate ligands into a three polyhedra thick band. The {Na(H₂O)_n}⁺ groups occupy the interior of the band but are displaced from the centroid toward one face so as to project the aqua ligands into the extra-annular domain. The fluoride ligands bridge two vanadium sites as well as coordinating to the sodium cation.     

Synthesis of a ruthenium complex of a cyclic trifunctional η6, η1, η1-arene–diphosphine ligand by intramolecular dehydrofluorinative carbon–carbon coupling

Treatment of the ruthenium complex cation [(η⁶-C₆H₃Me₃-1,3,5)(RuCl(dfppe)]⁺ {dfppe=(C₆F₅)₂PCH₂CH₂P(C₆F₅)₂} with proton sponge yields [{η⁶,η¹,η¹-C₆H₃Me-5-[CH₂-2-C₆F₄P(C₆F₅)CH₂]₂-1,3}RuCl]⁺ by stepwise intramolecular dehydrofluorinative carbon–carbon coupling.     

Synthesis and Redox Properties of an Electropolymerizable Amido Ferrocenyl Pyrrole-functionalized Dendrimer

A novel diaminobutane-based poly(propyleneamine) ferrocenyl dendrimer functionalized with electrochemically polymerizable pyrrole substituents, DAB-dend-[{η⁵-C₅H₄CONH}Fe{η⁵-C₅H₄C(O)NH(CH₂)₃NC₄H₄}]₄ (1), has been prepared and characterized. A secondary reaction product, the dipyrrole derivative [Fe{η⁵-C₅H₄C(O)NH(CH₂)₃NC₄H₄}₂] (2) has been also isolated and used as a model to facilitate the characterization of 1. The molecular structure of 2 has been determined by single crystal X-ray diffraction studies. Glassy carbon electrodes have been successfully modified by electropolymerization of the pyrrole-functionalized derivatives 1 and 2, in dichloromethane/acetonitrile solutions, resulting in visually detectable electroactive ferrocenyl polymer films persistently attached to the electrode surfaces. Osteryoung square wave voltammetry experiments (OSWV) showed that films of the electropolymerized amidoferrocenylpyrrole functionalized dendrimer 1 (poly-1) senses H₂PO₄⁻ in aqueous solution using Li[B(C₆F₅)₄] as supporting electrolyte. This paper is dedicated to Professor Didier Astruc in “recognition” of his outstanding contributions to so many fields of inorganic and organic chemistry. Furthermore, CMC and BA thank him for his counsel and friendship during and after their post doctoral stages in his lab.     

Analysis of the kinetics for the H2 + - \frac{1}{2}O2 ⇌ H2O reaction on a hot Pt surface in the pressure range 0.10–10 Torr

The H₂ + O₂ ⇌ H₂O reaction on platinum at 700 and 1300 K has been studied. A stagnation flow geometry was used with a gas mixture of H₂ and O₂ at pressures between 0.10 and 10 Torr. Comparing SHG results with simulations using different reaction parameters, it was concluded that , and . LIF measurements showed an ambiguity in the choice of main water-producing channel. Both hydrogen addition with low sticking coefficients and hydroxyl disproportionation with high sticking coefficients are plausible. This revised version was published online in July 2006 with corrections to the Cover Date.     

Particle size from optical anisotropy effects in scattered light

An original light-scattering method often suitable for the case of anisotropic particles is explained. Two particular values of the scattering angle θ are needed: θ_m, the angular position of the minimum of the H_h component, and θ_o, the angular value for which H_h = V_v. This method has been successfully applied to the case of copolymer single crystals.